Why was the State of Washington named after George Washington?

As an act of respect.

2nd Answer:

The original name that the territory wanted to use was either Lincoln State or Columbia State. (It is south and touching British Columbia) They threw Lincoln out as a name for some reason.

Someone pointed out that the name Columbia would be confused with "District of Columbia". So in a brilliant epiphany, they decided to use the name Washington instead.

. . . for the reason mentioned above.